Remainder Theorem
What is Remainder Theorem?
According to Remainder Theorem, for any polynomial p(x) (whose degree is greater than equal to 1) when divided by the linear polynomial (x – a), the remainder is always p(a).
Who Invented Remainder Theorem?
The credit for inventing remainder theorem goes to Chinese mathematician Sun Zi and the it was completed by Qin Jiushao in 1247.
What is the Use of Factor Theorem?
Factor theorem is used to find the factors of the given polynomial. For any polynomial f(x), x-a is the factor of the polynomial f(x) only when, f(a) is zero.
What are Applications of Remainder Theorem?
Remainder theorem is widely used to find the remainder of the polynomial without actually performing the long division and remainder theorem along with factor theorem is widely used to solve the polynomial equation.
What is Remainder Theorem Formula?
For the polynomial p(x) when divided by the linear polynomial (ax+b) the Remainder Theorem Formula is
p(x) / (ax + b)
Remainder = p (-b/a)
Remainder Theorem
Remainder Theorem is the basic theorem used in mathematics which is used to find the remainder of any polynomial when it is divided by a linear polynomial. The remainder theorem works on the principle of Euclidean Division Lemma.
But the remainder theorem also has some limitations, i.e. it works only when a polynomial is divided by a linear polynomial, else it fails. The remainder Theorem is exclusively mentioned for Class 9 students. Now let’s learn about the Reminder theorem, its proof, and others in detail in this article.
Table of Content
- What is the Remainder Theorem?
- Remainder Theorem Definition
- Remainder Theorem Formula
- Remainder Theorem Statement
- Remainder Theorem Proof
- Dividing a Polynomial by a Non-Zero Polynomial
- Remainder Theorem of Polynomial
- Euler Remainder Theorem
- Factor Theorem
- Remainder Theorem and Factor Theorem
- Remainder Theorem Examples